Question

Let (X,Y) have the joint pdf $f(x,y) = \frac{1}{3} + x^2 + y^2$, $0 < x < 1$, $0 < y < 1$, zero elsewhere. Find Cov(X,Y).

Name: let xy have the joint pdf fxy frac13 x2 y2 0 x 1 0 y 1 zero elsewhere find covxy 18481
Uploaded: 2021-11-01T20:06:30-08:00
Duration: 10 min 29 s
Channel: Satyam Gupta
Description: let xy have the joint pdf fxy frac13 x2 y2 0 x 1 0 y 1 zero elsewhere find covxy 18481

          Let (X,Y) have the joint pdf $f(x,y) = \frac{1}{3} + x^2 + y^2$, $0 < x < 1$, $0 < y < 1$, zero elsewhere.
Find Cov(X,Y).

$let xy have the joint pdf fxy frac13 x2 y2 0 x 1 0 y 1 zero elsewhere find covxy 18481$

Added by Joe R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Satyam Gupta

11/01/2021

Step 1

Recall that Cov(X,Y) = E[XY] - E[X]E[Y]. First, we find E[X]. $E[X] = \int_{0}^{1} \int_{0}^{1} x f(x,y) dx dy = \int_{0}^{1} \int_{0}^{1} x (\frac{1}{3} + x^2 + y^2) dx dy = \int_{0}^{1} \int_{0}^{1} (\frac{x}{3} + x^3 + xy^2) dx dy$ $E[X] = \int_{0}^{1} Show more…

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